+

Place Value

+Numbers in Everyday Life

Where do we see them?

What do they represent?

What do they mean?

+Numbers

Numbers can be written in three ways: 1) standard form- standard digits 2) word form-when a number is written out in words 3) expanded form- as a sum of the all of the digits’ place

values

+Standard Form

Standard Form- written with digits

45 781359087

365 430576

+Word Form

Word form- when a number is written out in words

Five five hundred ninety six

one hundred three thousand

*NOTE: THERE IS NO AND IN WORD FORM UNLESS THERE ARE DECIMALS

+Expanded Form

Expanded form- a sum of the all of the digits’ place value

98

We have a 9 in the tens place and an 8 in the ones place

9(10)+8(1)=

90+8=98

19,875

We have a 5 in the ones place, a 7 in the tens place, an 8 in the hundreds place, a 9 in the thousands place, and a 1 in the ten thousands place

1(10,000)+9(1,000)+8(100)+7(10)+5(1)

10,000+9,000+800+70+5=19,875

+Which Form?

57

Three hundred

4(10,000)+6(1,000)+6(100)+3(10)+2(1)

seven hundred ninety-seven thousand nine

two hundred three thousand three

6789362

6( 1,000,000) + 2(100,000) + 6(10,000) + 3( 1,000) + 9 (100) + 8(10) + 1(1)

4(1,000,000) + 3(100,000) + 2(10,000) + 8(1,000) + 8(100) + 3(10) + 4 (1)

+Place Value Place value-the value of where the digit is in the number

Think how many sets!

+Place Value

When we look at a number we can learn three things about each digit:1) what place value it is

2) what it means to be in that place value

3) value of the digit

+Let’s Practice What do we know about the underlined digit?

6754

in the ones place

means there are 4 ones

there is a value of 4

Lets write the expanded form:

6(1000)+7(100)+5(10)+4(1)

6000+700+50+4

 

+Let’s Practice What do we know about the underlined digit?

6,589,321

in the billions place

there are 6 sets of billions

there is a value of 6 billion 

+Let’s Practice What do we know about the underlined digit?

2,145

it is in the hundreds place

there is 1 set of a hundred

there is a value of 100

Lets write the expanded form:

2(1000)+1(100)+4(10)+5(1)

2000+100+40+5

 

+Let’s PracticeWhat do we know about the underlined

digit?

6,832

1)

2)

3)

Lets write the expanded form:

 

+Let’s PracticeWhat do we know about the underlined

digit?

38,214

1)

2)

3)

Lets write the expanded form:

 

+Let’s PracticeWhat do we know about the underlined

digit?

123,965

1)

2)

3)

Lets write the expanded form:

 

+Let’s PracticeWhat do we know about the underlined

digit?

421,795,087

1)

2)

3)

Lets write the expanded form:

 

+You Try

Provide the information for the underlined digit and then the expanded form for the number.

43,205,678

586

102,549,873

+Which has a larger value?

4567 or 6321

Remember when we think place value we think about how many sets the digit represents

The 6 in 6321 has a greater value because 6 is in the thousands place meaning it has a value of 6,0000 (6x1000) compared to the 6 in 4567 which is in the tens place and has a value of 60 (6x10).

+Which has a larger value?

429589 or 301

Remember when we think place value we think about how many sets the digit represents

The 9 in 429589 has a smaller value because 9 is in the ones place meaning it has a value of 9 (9x1) compared to the 3 in 301 which is in the hundreds place and has a value of 300 (3x100).

+Which has a larger value

58,212,367 vs 1,092,850

197 vs 9928

284,541 vs 925,755 =

+You try! Which has a larger value 993,124 vs 831,868

213, 404,323 vs 226,384

796,834 vs 914,227

+Practice! Using the number sticks, pick 9 numbers. It is up to you

and your partner to place your numbers strategically so you can make the biggest and smallest numbers possible!

You must explain how you know the it is the biggest number and the smallest number possible (expanded form).

+Game Time

Play against your partner and try to create the biggest number! Use number sticks to get 6 digits and use those digits to create your number. On a separate sheet of paper state who’s number was larger and why.

+Before You Go

On a piece of paper they need to construct a 9 digit number, only having one 0. Provide the place, what it means, and the value of each digit and then write the expanded form of the number.